z3/src/test/pdd.cpp

#include "math/dd/dd_pdd.h"

namespace dd {
static void test1() {
    pdd_manager m(3);
    pdd v0 = m.mk_var(0);
    pdd v1 = m.mk_var(1);
    pdd v2 = m.mk_var(2);
    std::cout << v0 << "\n";
    std::cout << v1 << "\n";
    std::cout << v2 << "\n";
    pdd c1 = v0 * v1 * v2;
    pdd c2 = v2 * v0 * v1;
    std::cout << c1 << "\n";
    SASSERT(c1 == c2);

    c1 = v0 + v1 + v2;
    c2 = v2 + v1 + v0;
    std::cout << c1 << "\n";
    SASSERT(c1 == c2);

    c1 = (v0+v1) * v2;
    c2 = (v0*v2) + (v1*v2);
    std::cout << c1 << "\n";
    SASSERT(c1 == c2);
    c1 = (c1 + 3) + 1;
    c2 = (c2 + 1) + 3;
    std::cout << c1 << "\n";
    SASSERT(c1 == c2);
    c1 = v0 - v1;
    c2 = v1 - v0;
    std::cout << c1 << " " << c2 << "\n";

    c1 = v1*v2;
    c2 = (v0*v2) + (v2*v2);
    pdd c3 = m.zero();
    VERIFY(m.try_spoly(c1, c2, c3));
    std::cout << c1 << " " << c2 << " spoly: " << c3 << "\n";

    c1 = v1*v2;
    c2 = (v0*v2) + (v1*v1);
    VERIFY(m.try_spoly(c1, c2, c3));
    std::cout << c1 << " " << c2 << " spoly: " << c3 << "\n";

    c1 = (v0*v1) - (v0*v0);
    c2 = (v0*v1*(v2 + v0)) + v2;
    c3 = c2.reduce(c1);
    std::cout << c1 << " " << c2 << " reduce: " << c3 << "\n";
}

static void test2() {
    std::cout << "\ntest2\n";
    // a(b^2)cd + abc + bcd + bc + cd + 3 reduce by  bc
    pdd_manager m(4);
    pdd a = m.mk_var(0);
    pdd b = m.mk_var(1);
    pdd c = m.mk_var(2);
    pdd d = m.mk_var(3);
    pdd e = (a * b * b * c * d) + (2*a*b*c) + (b*c*d) + (b*c) + (c*d) + 3;
    std::cout << e << "\n";
    pdd f = b * c;
    pdd r_ef = m.reduce(e, f);
    m.display(std::cout);
    std::cout << "result of reduce " << e << " by " << f << " is " << r_ef <<  "\n";
    pdd r_fe = m.reduce(f, e);
    std::cout << "result of reduce " << f << " by " << e << " is " << r_fe << "\n" ;
    VERIFY(r_fe == f);
}

static void test3() {
    std::cout << "\ntest3\n";
    pdd_manager m(4);
    pdd a = m.mk_var(0);
    pdd b = m.mk_var(1);
    pdd c = m.mk_var(2);
    pdd d = m.mk_var(3);
        
    pdd e = a + c;
    for (unsigned i = 0; i < 5; i++) {
        e = e * e;
    }
    e = e * b;
    std::cout << e << "\n";
}

static void test_reset() {
    std::cout << "\ntest reset\n";
    pdd_manager m(4);
    pdd a = m.mk_var(0);
    pdd b = m.mk_var(1);
    pdd c = m.mk_var(2);
    pdd d = m.mk_var(3);
    std::cout << (a + b)*(c + d) << "\n";

    unsigned_vector l2v;
    for (unsigned i = 0; i < 4; ++i) 
        l2v.push_back(3 - i);
    m.reset(l2v);
    a = m.mk_var(0);
    b = m.mk_var(1);
    c = m.mk_var(2);
    d = m.mk_var(3);
    std::cout << (a + b)*(c + d) << "\n";
}

static void test5() {
    std::cout << "\ntest5\n";
    pdd_manager m(2);
    pdd a = m.mk_var(0);
    pdd b = m.mk_var(1);

    pdd e = (a - b) * ( a + b);
    pdd f = a * a  - b * b;
    SASSERT(e == f);

    e = (a - b)* (a - b);
    f = a * a - 2 * a * b + b * b;
    SASSERT(e == f);
    e = a - 3;
    e = e * e;
    f = a * a - 6 * a + 9;
    SASSERT(e == f);        
    e = 2 * a - 3;
    e = e * e;
    f = 4 * a * a - 12 * a + 9;
    SASSERT(e == f);        
}


void test_iterator() {
    std::cout << "test iterator\n";
    pdd_manager m(4);
    pdd a = m.mk_var(0);
    pdd b = m.mk_var(1);
    pdd c = m.mk_var(2);
    pdd d = m.mk_var(3);
    pdd p = (a + b)*(c + 3*d) + 2;
    std::cout << p << "\n";
    for (auto const& m : p) {
        std::cout << m << "\n";
    }
}
class test {
public :
    static void order() {
    std::cout << "order\n";
    pdd_manager m(4);
    unsigned va = 0;
    unsigned vb = 1;
    unsigned vc = 2;
    unsigned vd = 3;
    pdd a = m.mk_var(va);
    pdd b = m.mk_var(vb);
    pdd c = m.mk_var(vc);
    pdd d = m.mk_var(vd);
    pdd p = a + b;
    std::cout << p << "\n";
    unsigned i = 0;
    for (auto const& m : p) {
        std::cout << m << "\n";        
        SASSERT(i != 0 ||( m.vars.size() == 1 && m.vars[0] == vb));
        SASSERT(i != 1 ||( m.vars.size() == 1 && m.vars[0] == va));
        i++;
    }
    pdd ccbbaa = c*c*b*b*a*a;
    pdd ccbbba = c*c*b*b*b*a;
    p = ccbbaa + ccbbba;

    i = 0;
    std::cout << "p = " <<  p << "\n";
    for (auto const& m : p) {
        std::cout << m << "\n";
        SASSERT(i != 0 ||( m.vars.size() == 6 && m.vars[4] == vb)); // the first one has to be ccbbba
        SASSERT(i != 1 ||( m.vars.size() == 6 && m.vars[4] == va)); // the second one has to be ccbbaa
        i++;
    }
    pdd dcbba = d*c*b*b*a;
    pdd dd = d * d;
    p = dcbba + ccbbba + dd;
    vector<unsigned> v;
    std::cout << "p = " <<  p << "\n";
    unsigned k = p.index();
    std::cout << "pdd(k) = " << pdd(k, m) << "\n";
    k = m.first_leading(k);
    do {
        if (m.is_val(k)) {
            SASSERT(m.val(k).is_one());
            break;
        }
        v.push_back(m.var(k));        
        std::cout << "pdd(k) = " << pdd(k, m) << "\n";
        std::cout << "push v" << m.var(k) << "\n";
        k = m.next_leading(k);
    } while(true);
    auto it = v.begin();
    std::cout << "v" << *it;
    it++;
    for( ; it != v.end(); it ++) {
        std::cout << "*v" << *it;
    }
    SASSERT(v.size() == 6);
    SASSERT(v[0] == vc);
    std::cout << "\n";
    v.reset();
    p = d*c*c*d + b*c*c*b + d*d*d;
    k = p.index();
    std::cout << "pdd(k) = " << pdd(k, m) << "\n";
    k = m.first_leading(k);
    do {
        if (m.is_val(k)) {
            SASSERT(m.val(k).is_one());
            break;
        }
        v.push_back(m.var(k));        
        std::cout << "pdd(k) = " << pdd(k, m) << "\n";
        std::cout << "push v" << m.var(k) << "\n";
        k = m.next_leading(k);
    } while(true);
    it = v.begin();
    std::cout << "v" << *it;
    it++;
    for( ; it != v.end(); it ++) {
        std::cout << "*v" << *it;
    }
    SASSERT(v.size() == 4);
    SASSERT(v[0] == vd);
    std::cout << "\n";
    
}
};

}

void tst_pdd() {
    dd::test1();
    dd::test2();
    dd::test3();
    dd::test5();
    dd::test_reset();
    dd::test_iterator();
    dd::test::order();
}